Score:0

ZKP but the verifier knows all possible secrets

in flag

Is there a (preferably simple) implementation of ZKP where the verifier already knows the set of possible secrets? Especially if the set is very small (even as few as 2 or 3 options). The prover must convince the verifier that she possesses one of the secrets, but not which one.

István András Seres avatar
cf flag
What is exactly the statement you want to prove in zero-knowledge?
SEJPM avatar
us flag
The question is a bit confusing to me. Usually with ZKPs you prove that you know some $w$ for some public $x$ such that some function $F(x,w)$ returns true. How many such valid $w$ there are for each $x$ is up to $F$ and it can be as low as $1$. There are also more composite variants which may be what you want where you prove that you know _one_ $w$ for a list of $x_i$ such that $\exists i: F(x_i,w)=1$.
homamo2050 avatar
in flag
Simply put, the verifier knows a secret set, let's say $\{ 123, 456 \}$. The prover wants to prove that she is aware of (at least) one element from that set, without disclosing which one. How can I improve the question?
Score:1
in flag

The statement to prove could be like, the secret committed is one from a set of secrets committed earlier. Probably "OR protocol" would fit such a scenario.

Geoffroy Couteau avatar
cn flag
unless I misunderstood the question, the "secret" here also includes the randomness of the commitment. By my understanding, what the OP asks about is for proofs with a small number of possible witnesses - which are always trivial
Vadym Fedyukovych avatar
in flag
This is my understanding too: a small set of secrets and sigma protocols instantiated for each such secret/witness, OR-connected according to Cramer-Damgard-Schoenmakers paper.
Geoffroy Couteau avatar
cn flag
ha, my comment is not correct then, I now understand OP's question with the clarification in their comment, and I think your answer is correct
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